Spatial Econometric Analysis Using GAUSS 10 Kuan-Pin Lin Portland State University

Spatial Panel Data Models The General Model

Spatial Panel Data Models Assumptions Fixed Effects Random Effects Spatial Error Model: A=I or =0 Spatial Lag Model: B=I or  =0 Panel Data Model: A=B=I

Spatial Panel Data Models Example: U. S. Productivity (48 States, 17 Years) Panel Data Model ln(GSP) =   +   ln(Public) +  2 ln(Private) +  3 ln(Labor) +  4 (Unemp) +   u + v Spatial Lag Model ln(GSP) =   +   ln(Public) +  2 ln(Private) +  3 ln(Labor)+  4 (Unemp) + λW ln(GSP) +   u + v Spatial Error Model ln(GSP) =   +   ln(Public) +  2 ln(Private) +  3 ln(Labor) +  4 (Unemp) +   W   e  e  u + v Spatial Mixed Model ln(GSP) =   +   ln(Public) +  2 ln(Private) +  3 ln(Labor) +  4 (Unemp) + λW ln(GSP) +   W   e  e  u + v

Model Estimation Based on panel data models (pooled, fixed effects, random effects), we consider: Spatial Error Model Spatial Lag Model Spatial Mixed Model Model Estimation Generalized Least Squares (IV/GLS) Generalized Method of Moments (GMM/GLS) Maximum Likelihood Estimation

Spatial Lag Model Estimation The Model: SPLAG(1) OLS is biased and inconsistent.

Spatial Lag Model Estimation Fixed Effects

Spatial Lag Model Estimation Fixed Effects: IV or 2SLS Instrumental Variables Two-Stage Least Squares

Spatial Lag Model Estimation Random Effects

Spatial Lag Model Estimation Random Effects: IV/GLS Instrumental Variables Two-Stage Generalized Least Squares

Spatial Lag Model Estimation Random Effects: IV/GLS Feasible Generalized Least Squares Estimate  v 2 and  u 2 from the fixed effects model: FGLS for random effects model:

Spatial Error Model Estimation The Model: SPAR(1) Fixed Effects Random Effects

Spatial Error Model Estimation Fixed Effects Moment Functions

Spatial Error Model Estimation Fixed Effects The Model: SPAR(1) Estimate  and  iteratively: GMM/GLS OLS GMM GLS

Spatial Error Model Estimation Random Effects Moment Functions (Kapoor, Kelejian and Prucha, 2006)

Spatial Error Model Estimation Random Effects The Model: SPAR(1) Estimate  and  iteratively: GMM/GLS OLS GMM GLS

Spatial Mixed Model Estimation The Model: SARAR(1,1)

Spatial Mixed Model Estimation Two-Stage Estimation Sample moment functions are the same as in the spatial error AR(1) model. The efficient GMM estimator follows exactly the same as the spatial error AR(1) model. The transformed model which removes spatial error AR(1) correlation is estimated the same way as the spatial lag model using IV and GLS.

Spatial Mixed Model Estimation Fixed Effects The Model: SPARAR(1,1)

Spatial Mixed Model Estimation Fixed Effects Estimate  and  iteratively: GMM/GLS IV/2SLS GMM GLS

Spatial Mixed Model Estimation Random Effects The Model: SPARAR(1,1)

Spatial Mixed Model Estimation Random Effects Estimate  and  iteratively: GMM/GLS IV/2SLS GMM GLS

Example: U. S. Productivity Baltagi (2008) [munnell.5]munnell.5 Spatial Panel Data Model: GMM/GLS (Spatial Error) ln(GSP) =   +   ln(Public) +  2 ln(Private) +  3 ln(Labor) +  4 (Unemp) +  =ρW  + e, e = i  u + v Fixed Effectss.e Random Effectss.e   0.202* *0.021 3 * *0.025 4 * *0.001 0 *0.136 ρ0.578* *0.060

Example: U. S. Productivity Baltagi (2008) [munnell.5]munnell.5 Spatial Panel Data Model: GMM/GLS (Spatial Mixed) ln(GSP) =   +   ln(Public) +  2 ln(Private) +  3 ln(Labor) +  4 (Unemp) + λW ln(GSP) +  =ρW  + e, e = i  u + v Fixed Effectss.e Random Effectss.e   0.185* *0.022 3 * *0.026 4 * *0.001 0 *0.174 λ0.093* *0.015 ρ0.488* *0.059

Another Example China Provincial Productivity [china.9]china.9 Spatial Panel Data Model: GMM/GLS (Spatial Error) ln(Q) =  +  ln(L) +  ln(K) +   =ρW  + e, e = i  u + v Fixed Effectss.e Random Effectss.e    ρ

Another Example China Provincial Productivity [china.9]china.9 Spatial Panel Data Model: GMM/GLS (Spatial Mixed) ln(Q) =  +  ln(L) +  ln(K) +  W ln(Q) +   =ρW  + e, e = i  u + v Fixed Effectss.e Random Effectss.e    λ ρ

Maximum Likelihood Estimation Error Components Assumptions Fixed Effects: Random Effects:

Maximum Likelihood Estimation Fixed Effects Log-Likelihood Function

Maximum Likelihood Estimation Fixed Effects Log-Likelihood Function (Lee and Yu, 2010) Where z* is the transformation of z using the orthogonal eigenvector matrix of Q.

Maximum Likelihood Estimation Random Effects Log-Likelihood Function

Example: U. S. Productivity Baltagi (2008) [munnell.4]munnell.4 Spatial Panel Data Model: QML (Spatial Lag) ln(GSP) =   +   ln(Public) +  2 ln(Private) +  3 ln(Labor) +  4 (Unemp) + λW ln(GSP) + ,  = i  u + v Fixed Effectss.e Random Effectss.e   0.187* *0.025 3 * *0.029 4 * * 0 *0.166 λ0.275* *0.029

Example: U. S. Productivity Baltagi (2008) [munnell.4]munnell.4 Spatial Panel Data Model: QML (Spatial Error) ln(GSP) =   +   ln(Public) +  2 ln(Private) +  3 ln(Labor) +  4 (Unemp) +  =ρW  + e, e = i  u + v Fixed Effectss.e Random Effectss.e   0.205* *0.023 3 * *0.027 4 * *0.001 0 ρ0.557* *0.033

Example: U. S. Productivity Baltagi (2008) [munnell.4]munnell.4 Spatial Panel Data Model: QML (Spatial Mixed) ln(GSP) =   +   ln(Public) +  2 ln(Private) +  3 ln(Labor) +  4 (Unemp) + λW ln(GSP) +  =ρW  + e, e = i  u + v Fixed Effectss.e Random Effectss.e   0.191* *0.023 3 * *0.027 4 * *0.001 0 *0.212 λ ρ0.455* *0.038

Another Example China Provincial Productivity [china.8]china.8 Spatial Panel Data Model: QML (Spatial Lag) ln(Q) =  +  ln(L) +  ln(K) +  W ln(Q) +   = i  u + v Fixed Effectss.e Random Effectss.e    λ

Another Example China Provincial Productivity [china.8]china.8 Spatial Panel Data Model: QML (Spatial Error) ln(Q) =  +  ln(L) +  ln(K) +   =ρW  + e, e = i  u + v Fixed Effectss.e Random Effectss.e    ρ

Another Example China Provincial Productivity [china.8]china.8 Spatial Panel Data Model: QML (Spatial Mixed) ln(Q) =  +  ln(L) +  ln(K) +  W ln(Q) +   =ρW  + e, e = i  u + v Fixed Effectss.e Random Effectss.e    λ ρ

References Elhorst, J. P. (2003). Specification and estimation of spatial panel data models, International Regional Science Review 26, Kapoor M., Kelejian, H. and I. R. Prucha, “Panel Data Models with Spatially Correlated Error Components,” Journal of Econometrics, 140, 2006: Lee, L. F., and J. Yu, “Estimation of Spatial Autoregressive Panel Data Models with Fixed Effects,” Journal of Econometrics 154, 2010: